What is the product of all positive factors of 18? A. 324 B. 5832 C. 39 D. 1521 E. 3042 The correct answer is 5832. Choice B. Let us first focus on how to find the answer methodically and then understand why the method works. The How? Step 1: Find the number of factors for 18. Step 1a. Express 18 as a product of its prime factors. 18 = 2 * 3^2 Step 1b. Increment the … [Read more...] about Number Properties – Product of factors
GMAT Problem Solving
Number Properties – divisibility and remainders
When a positive integer A is divided by 5 and 7, the remainders obtained are 3 and 4, respectively. When the positive integer B is divided by 5 and 7, the remainders obtained are 3 and 4, respectively. Which of the following is a factor of (A - B)? (A) 12 (B) 24 (C) 35 (D) 16 (E) 30 Correct Answer : Choice C Explanatory Answer When A is divided by 5, the remainder is 3. So, … [Read more...] about Number Properties – divisibility and remainders
Number properties – Factorial
How many trailing zeroes does 60! have?(A) 12(B) 9(C) 15(D) 14(E) 13 … [Read more...] about Number properties – Factorial
Permutation of Digits & Divisibility
This is an interesting counting methods question that combines a very basic rule of test of divisibility of number by 3. Question How many six digit positive integers comprising only the digits 1 and 2 can be formed such that the number is divisible by 3? 3 20 22 38 360 Correct Answer Choice C. 22 such numbers can be formed. Video Explanation Explanatory … [Read more...] about Permutation of Digits & Divisibility
Equations – roots and powers
How many roots does x6 –12x4 + 32x2 = 0 have?(A) 1(B) 3(C) 4(D) 5(E) 2Solution:x^6 –12(x^4) + 32(x^2) = x^2 (x^4 – 12x^2 + 32) = x^2 (x^2 – 4)(x^2 – 8)The roots are 0, ±2, and ±2√2: a total of 5.Please remember that ‘0’ is also a root.The correct answer is D … [Read more...] about Equations – roots and powers